In communications and computing systems, many system resources are shared for use by large numbers of devices. For example, shared resources are commonplace in wireless, wireline, LAN, WAN, WIMAX, Blue Tooth wireless mobile communications systems, in which resources or pools of resources (hereinafter “resources” collectively) such as network elements, base stations, networks, servers, communications media, etc. are shared among multiple devices that require access to or continued utilization of the shared resources. Resource contention can occur in mobile communications systems such as Evolution Data Only (EVDO)-wireless networks, when multiple cell phones, PDAs, portable computers, etc. attempt to simultaneously access a local base station resource such that the input handling capacity of the base station is exceeded (access attempt failure), or when the base station is operating at maximum capacity and is unable to service any additional information from one or more currently served devices (utilization attempt failure). Contention may arise when multiple mobiles simultaneously attempt to access the base station on the access channel, leading to a collision of the call initiation messages. When a mobile device fails to obtain access or utilization of the base station, an internal apersistence system will cause the mobile to back off and refrain from further attempts for a given amount of time, where the time is determined according to an apersistence value provided by the base station resource or an apersistence control system associated therewith. By selecting the apersistence values, the apersistence control system sets the back off behavior of the mobile devices in a manner that ideally maximizes the access and utilization of the base station resource, and may also support multiple priority classes with different apersistence for each class. To accurately determine the apersistence values sent to the mobile devices, the apersistence control system must have data or information regarding the amount of incoming traffic such as requests for access or utilization of the access channel for a base station resource. In this regard, the mobile devices in EVDO systems send access probe requests to the base station access channel in discrete timeslots, and incoming traffic estimation systems may be constructed to operate on timeslot information that indicates whether a particular timeslot was empty (no access probe packets), or contained either a successful single probe or a collision of multiple probe packets. Thus, there is a need for techniques and systems to distinguish between the three possible conditions in a given timeslot in an unambiguous and robust way to facilitate implementation of traffic estimation systems and control systems for adjusting the resource to minimize collisions.